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The geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…

Quantum Physics · Physics 2024-11-07 Jun-Feng Ren , Jing Li , Hai-Tao Ding , Dan-Wei Zhang

The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…

Quantum Physics · Physics 2023-10-02 Balázs Hetényi , Péter Lévay

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric…

This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…

Quantum Physics · Physics 2023-02-27 Sergio B. Juárez

The geometry of multi-parameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the…

Disordered Systems and Neural Networks · Physics 2021-05-25 Alexander-Georg Penner , Felix von Oppen , Gergely Zarand , Martin R. Zirnbauer

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…

Mathematical Physics · Physics 2010-10-12 P. Aniello , J. Clemente-Gallardo , G. Marmo , G. F. Volkert

In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for…

Mathematical Physics · Physics 2019-09-04 Marcelo Losada , Ignacio S. Gomez , Federico Holik

The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…

Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a…

Quantum Physics · Physics 2013-04-08 Ran Cheng

Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play…

Mesoscale and Nanoscale Physics · Physics 2022-01-12 Bruno Mera , Anwei Zhang , Nathan Goldman

We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields…

Mathematical Physics · Physics 2011-01-05 P. Aniello , J. Clemente-Gallardo , G. Marmo , G. F. Volkert

From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…

Statistical Mechanics · Physics 2013-09-04 Michael Kolodrubetz , Vladimir Gritsev , Anatoli Polkovnikov

The Berry curvature characterizes one aspect of the geometry of quantum states. It materializes, among other consequences, as an anomalous velocity of wave packets. In non-Hermitian systems, wave packet dynamics is enriched by additional…

Quantum Physics · Physics 2025-03-19 Jan Behrends , Roni Ilan , Moshe Goldstein

In this work, we review different generalizations of the quantum geometric tensor (QGT) in two-band non-Hermitian systems and propose a protocol for measuring them in experiments. We present the generalized QGT components, i.e. the quantum…

Mesoscale and Nanoscale Physics · Physics 2024-02-20 Y. -M. Robin Hu , Elena A. Ostrovskaya , Eliezer Estrecho

We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…

General Relativity and Quantum Cosmology · Physics 2024-03-20 J. L. Alonso , C. Bouthelier-Madre , J. Clemente-Gallardo , D. Martínez-Crespo

The quantum geometric tensor (QGT) characterizes the local geometry of quantum states, and its components directly account for the dynamical effects observed, e.g., in condensed matter systems. In this work, we address the problem of…

Mesoscale and Nanoscale Physics · Physics 2025-02-18 Y. -M. Robin Hu , Elena A. Ostrovskaya , Eliezer Estrecho

A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…

General Relativity and Quantum Cosmology · Physics 2009-10-30 Dorje C. Brody , Lane P. Hughston

The quantum geometric tensor (QGT) fundamentally encodes the geometry and topology of quantum states in both Hermitian and non-Hermitian regimes. While adiabatic perturbation theory links its real part (quantum metric) and imaginary part…

Quantum Physics · Physics 2025-12-19 Ze-Hao Huang , Hai-Tao Ding , Li-Jun Lang

We experimentally observe the quantum geometric tensor, namely the quantum metric and the Berry curvature, for a square lattice of radiatively coupled plasmonic nanoparticles. We observe a non-zero Berry curvature and show that it arises…

The geometry of quantum states can be an indicator of criticality, yet it remains less explored under non-Hermitian topological conditions. In this work, we unveil diverse scalings of the quantum geometry over the ground state manifold…

Strongly Correlated Electrons · Physics 2025-11-20 Y R Kartik , Jhih-Shih You , H. H. Jen
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